The combinatoric structure of the Feynman diagrams —entering the perturbative computation of \(Z_{SD}[B]\) — is illustrated in the simple case of the field theory models \(\phi ^3\)  and \(\phi ^4\)  in four dimensions in Section 2.
By means of the Wick contractions [1]}, [2]} of the field operators, we examine the Feynman diagrams which are associated with the expectation values (REF ). We demonstrate that the short distance behaviour of the products of the composite operator \(\delta S [\phi ] / \delta \phi (x)\)  —that in \(d\)  dimensional spacetime has dimension \((d-1)\) — is really determined by the ultraviolet properties of operators of dimensions \((d-2)\)  and/or \((d-3)\) . For instance, when the interacting lagrangian entering the action \(S[\phi ]\)  is a cubic function of a scalar field \(\phi (x)\) , \(Z_{SD}[B]\)  can be related to the ordinary generating functional \(Z[J]\)  of correlation functions of the field \(\phi (x)\) . In general, it turns out that the connected component of \(Z_{SD}[B]\)  is the union of a local functional of \(B(x)\)  and a non-local part which is specified by the expectation values of field components \(\phi (x)\)  and possibly \(\phi ^2(x)\) .
